Figure 3.

Numerical results for quantum state tomography. (a–c) Plot of the fidelity between an unknown Haar random state $|\psi ⟩$ and its reconstructed state $|\varphi (\mathit{\theta })⟩$ for different $\mathcal{W}$ structures: ${\mathcal{W}}_{\mathrm{chain}}$ (a), ${\mathcal{W}}_{\mathrm{alternating}}$ (b), and ${\mathcal{W}}_{\mathrm{all}-\mathrm{to}-\mathrm{all}}$ (c). For each case, we show the results for different optimizers: SGD, Adam, and QNG. Here we fixed $L=2$. (d–f) Plot of the fidelity similar as above for different L as shown in the colored parentheses (blue star, yellow dagger, green double dagger). Here, blue star is the optimal number of layers for the SGD, yellow dagger is the optimal number of layers for the Adam, and green double dagger is the optimal number of layers for the QNG. We choose the appropriate (blue star, yellow dagger, green double dagger) for each N and each $\mathcal{W}$ structure so that the fidelity gets its (possible) highest accuracy.